22-1: Induced Current -Electromagnetic inductionis the process of inducing a current in a circuit with a changing magnetic field.
-If a magnet moves toward or away from the circuit or the circuit moves toward or away from the magnet a current is induced.
-The separation of charges by the magnetic force induces an emf.
-For negative charges in the wire, the force is upward along the wire. For positive charges, the force is downward.
-The polarity of the induced emf depends on the direction in which the wire is moved through the magnetic field.
-The angle between a magnetic field and a circuit affects induction.
-The induced current is largest when the plane of the loop is perpendicular to the magnetic field, it is less when the plane is tilted into the field, and it is zerio when the plane is parallel to the magnetic field.
-Change in the number of magnetic field lines induces a current.
-The direction of an induced current can be found using the right hand rule.
-Lenz's Law:
The magnetic field of the induced current opposes the change in the applied magnetic field.
-Faraday's Law of Magnetic Induction:
emf= -NΔ[AB(cos θ)]/Δt
where N is the number of loops in a circuit, always a whole number
-Applications of Induction:
Door bells- When the button is pushed, a small light bulb briefly goes out, indicating that the circuit has been opened and that the current has been temporarily discontinued.
Tape recorders- A magnetic tape passes over a gap and becomes magnetized in a pattern that corresponds to both the frequency and the intensity of the sound signal entering the microphone.
22-2: Alternating Current, Generators, and Motors
-An electricgenerator is a device that uses mechanical energy to turn the loop and converts it into electrical energy.
-A generator produces a continuously changing emf.
-The maximum emf for a generator is found with this equation:
maximum emf=NABω
where A is the cross sectional area of the loops, B is magnetic field strength, and ω is is the angular frequency of magnetic loops.
-Alternating current, or ac, is the output current from a generator that changes its direction at regular intervals.
-The rate at which the coil in an ac generator determines the maximum generated emf.
-Effective current and potential difference are measured in ac currents.
-The quantity for the maximum emf can be written as the maximum potential difference ΔVmax, and the emf produced by a generator can be expressed as:
-The instantaneous current that changes with potential difference can be determined using the definition of resistance. The instantaneous current, i, is related to maximum current by:
-Alternating current can be converted to direct current.
-Slip rings are conducting rings connected to the ends of the loop that rotate the loop.
-Motorsare devices that convert electrical energy into mechanical energy.
-The back emf is the induced emf; the faster the coil rotates; the greater the back emf becomes.
-The faster the motor turns, the smaller the net potential difference across the motor, the smaller the net current in the coil becomes.
22-3: Inductance -Faraday's Law can be rewritten as -M(ΔI/Δt) where M is a constant called the mutual inductance of the two coil system. The equation holds as long as the coils remain unchanged with respect to each other.
-A transformer is a device that converts a small ac potential difference to a larger on or vise-versa.
-A transformer has two coils wound around a core of soft iron. The left coil has N1 turns (primary) while the one on the right is represented by N2 (secondary).
The transformer equation is:
ΔV2=(N2/N1)ΔV1 or
ΔV2/ΔV1=N2/N1
-Real transformers are not perfectly efficient, power losses do occur.
-Coils in gasoline engines are transformers, represented below:
The transformer here is the ignition coil.
Practice Problems:
1. A coil with 25 turns of wire is wrapped around a hollow tube with an area of 1.8 m^2. Each turn has the same area as the tube. A uniform magnetic field is applied at a right angle to the plane of the coil. If the field increases uniformly from 0.00 T to 0.55 T in 0.85 s, find teh magnitude of the induced emf in teh coil. If the resistance in the coil is 2.5 Ω, find the magnitude of the induced current in the coil.
2. A generator consists of exactly eight turns of wire, each with an area A=0.095 m^2 and a total resistance of 12 Ω. The loop rotates in a magnetic field of 0.55 T at a constant frequency of 60.0 Hz. Find the maximum induced emf and the maximum induced current in the loop.
3. A set-up transformer is used on a 120 V line to provide a potential difference of 2400 V. If the primary has 75 turns, how many turns must the secondary have?
22-1: Induced Current
-Electromagnetic induction is the process of inducing a current in a circuit with a changing magnetic field.
-If a magnet moves toward or away from the circuit or the circuit moves toward or away from the magnet a current is induced.
-The separation of charges by the magnetic force induces an emf.
-For negative charges in the wire, the force is upward along the wire. For positive charges, the force is downward.
-The polarity of the induced emf depends on the direction in which the wire is moved through the magnetic field.
-The angle between a magnetic field and a circuit affects induction.
-The induced current is largest when the plane of the loop is perpendicular to the magnetic field, it is less when the plane is tilted into the field, and it is zerio when the plane is parallel to the magnetic field.
-Change in the number of magnetic field lines induces a current.
-The direction of an induced current can be found using the right hand rule.
-Lenz's Law:
- The magnetic field of the induced current opposes the change in the applied magnetic field.
-Faraday's Law of Magnetic Induction:- emf= -NΔ[AB(cos θ)]/Δt
where N is the number of loops in a circuit, always a whole number-Applications of Induction:
22-2: Alternating Current, Generators, and Motors
-An electric generator is a device that uses mechanical energy to turn the loop and converts it into electrical energy.
-A generator produces a continuously changing emf.
-The maximum emf for a generator is found with this equation:
- maximum emf=NABω
where A is the cross sectional area of the loops, B is magnetic field strength, and ω is is the angular frequency of magnetic loops.-Alternating current, or ac, is the output current from a generator that changes its direction at regular intervals.
-The rate at which the coil in an ac generator determines the maximum generated emf.
-Effective current and potential difference are measured in ac currents.
-The quantity for the maximum emf can be written as the maximum potential difference ΔVmax, and the emf produced by a generator can be expressed as:
-The instantaneous current that changes with potential difference can be determined using the definition of resistance. The instantaneous current, i, is related to maximum current by:
-Alternating current can be converted to direct current.
-Slip rings are conducting rings connected to the ends of the loop that rotate the loop.
-Motors are devices that convert electrical energy into mechanical energy.
-The back emf is the induced emf; the faster the coil rotates; the greater the back emf becomes.
-The faster the motor turns, the smaller the net potential difference across the motor, the smaller the net current in the coil becomes.
22-3: Inductance
-Faraday's Law can be rewritten as -M(ΔI/Δt) where M is a constant called the mutual inductance of the two coil system. The equation holds as long as the coils remain unchanged with respect to each other.
-A transformer is a device that converts a small ac potential difference to a larger on or vise-versa.
-A transformer has two coils wound around a core of soft iron. The left coil has N1 turns (primary) while the one on the right is represented by N2 (secondary).
The transformer equation is:
- ΔV2=(N2/N1)ΔV1 or
- ΔV2/ΔV1=N2/N1
-Real transformers are not perfectly efficient, power losses do occur.-Coils in gasoline engines are transformers, represented below:
The transformer here is the ignition coil.
Practice Problems:
1. A coil with 25 turns of wire is wrapped around a hollow tube with an area of 1.8 m^2. Each turn has the same area as the tube. A uniform magnetic field is applied at a right angle to the plane of the coil. If the field increases uniformly from 0.00 T to 0.55 T in 0.85 s, find teh magnitude of the induced emf in teh coil. If the resistance in the coil is 2.5 Ω, find the magnitude of the induced current in the coil.
2. A generator consists of exactly eight turns of wire, each with an area A=0.095 m^2 and a total resistance of 12 Ω. The loop rotates in a magnetic field of 0.55 T at a constant frequency of 60.0 Hz. Find the maximum induced emf and the maximum induced current in the loop.
3. A set-up transformer is used on a 120 V line to provide a potential difference of 2400 V. If the primary has 75 turns, how many turns must the secondary have?
Answers:
1. emf= -29 V
I= -12 A
2. maximum emf= 1.6x10^2 V
Imax=13 A
3. N2=1500 turns
Bibliography:
"Holt Online Learning." Holt Online Learning. 5 June 2009 <http://my.hrw.com/tabnav/controller.jsp?isbn=0030724864>.
All pictures taken from "Holt Online Learning." Holt Online Learning. 5 June 2009 <http://my.hrw.com/tabnav/controller.jsp?isbn=0030724864>.